linear model selection analysis

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linear model selection analysis

Harriet Jamieson
Hello list,

I am attempting a selection analysis sensu Lande and Arnold (1983), where
the basic premise is to model relative fitness of individuals as a function
of standardised trait values, where the relative fitness is relative to the
mean (by dividing fitness values by the mean fitness value, so centred
around 1) and the standardised trait values are calculated as z scores,
i.e. = (trait - mean) / SD, so they are centred around zero. The idea is
that, in its simplest form with a single trait of interest, the results of
the model 'fitness ~ trait’ should give a coefficient for ‘trait’ that is a
selection gradient. My problem is that my ‘trait’ in this case is count
data, and it doesn’t seem appropriate to transform Poisson data into the
standardised trait variable as above. So my first question is whether this
is an appropriate way to treat count data?

I have considered three alternatives to work round this:
1. Plough ahead and transform the count data into the standardised trait
scores and do the analysis.
2. Use the raw count data as the trait variable, unstandardised - this
might be fine as a general linear model, but doesn’t give me sensible
estimates for selection gradients on the traits.
3. I tried looking for published work where count data was used in a
selection analysis - I’m sure I can’t be doing something that strange, but
I could only find one other example, and here they did something different,
where they actually turned the model around and modelled the trait as a
function of fitness, so trait ~ fitness, where fitness was relativised but
the trait was kept as count data and a Poisson distribution was specified.

I suppose if anyone has any specific experience of selection analysis, this
would be extremely helpful. More generally, however, I think I would like
some thoughts on the following questions:
1. Is it appropriate to z score transform count data? Why/why not?
2. If the basic model Y ~ X gives a coefficient for X that is the gradient,
then how is this interpretation of the coefficient affected if X is raw
count data?
3. Does the example I found where the model was flipped round give the same

I realise the problem is rather specific to a certain application of linear
models, but I would be grateful for any insight anyone could offer on how
these alternatives change the interpretation of the models.

Thanks very much in advance,

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